Maxwell symmetries and some applications

TL;DR

This paper develops a gauge theory based on Maxwell algebra, extending Poincaré symmetry, and applies it to formulate Maxwell gravity with potential cosmological implications, including a cosmological approximation.

Contribution

It introduces a local gauge theory of Maxwell algebra and constructs Maxwell gravity, integrating additional gauge fields into gravitational theory.

Findings

Maxwell gravity combines Einstein action with a generalized cosmological term.

A cosmological approximation involves two scalar fields from gauge fields.

Framework outlines potential for further theoretical developments.

Abstract

The Maxwell algebra is the result of enlarging the Poincar\'{e} algebra by six additional tensorial Abelian generators that make the fourmomenta non-commutative. We present a local gauge theory based on the Maxwell algebra with vierbein, spin connection and six additional geometric Abelian gauge fields. We apply this geometric framework to the construction of Maxwell gravity, which is described by the Einstein action plus a generalized cosmological term. We mention a Friedman-Robertson-Walker cosmological approximation to the Maxwell gravity field equations, with two scalar fields obtained from the additional gauge fields. Finally, we outline further developments of the Maxwell symmetries framework.